THE INFLUENCE OF ERRORS OF VELOCITY MEASUREMENTS ON THE RESULTS OF MÖSSBAUER SPECTRA FITTING

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THE INFLUENCE OF ERRORS OF VELOCITY MEASUREMENTS ON THE RESULTS OF

MÖSSBAUER SPECTRA FITTING

B. Gavrilov, B. Zemskov

To cite this version:

B. Gavrilov, B. Zemskov. THE INFLUENCE OF ERRORS OF VELOCITY MEASUREMENTS ON THE RESULTS OF MÖSSBAUER SPECTRA FITTING. Journal de Physique Colloques, 1980, 41 (C1), pp.C1-111-C1-112. �10.1051/jphyscol:1980120�. �jpa-00219688�

JOURNAL DE PHYSIQUE C0ff0que C1, suppfkment au n O 1, Tome 41, janvier 1980, page ~ 1 - 1 1 1

M E INFLUENCE OF ERRORS OF VELOCITY MEASUREENTS ON THE RESULTS OF @SBAUER SPECTRA FIlTING

3 . M . Gavrilov and B.G. Zemskov

S t a t e C o d t t e e f o r Standards o f USSR Minister CouciZ, 9, Leninsky Prospect, 117049, Moscow, USSR.

In the present work we investigated In the case of absolute method of spec- the influence of errors of velocity mea- trometer calibration is used /2,3/ the surements on the precision of Mbssbauer "measured" values of xi are simulated as

Xj m G ( v j , b X 3 ) 2 (4)

spectra parameters (MSP) determination by statistical simulation technique /1/.

The velocity values x measured by 3

Here

6 ,

characterizes the precision of velocity measurements by the abso1.ute 3 an experimentalist and used to fit a speo method. Supposing that Mbssbauer spectrum trum are not equal to the real velocity and its calibration characteristics were

measured simultaneously the spectrum is simulated according to eq. ( 2 ) with the values v In the case of relative method

j*

of Mbssbauer spectrometer calibration is

same v that are in eq. (4).

used the values of x are supposed to be

3

3

in some dependence (for example, in line- The spectra were simulated and fit- ar one) on the point number j. However, ted by two methods: the conventional le- ast-squares method (CLSM) and the "modi- fied" LSM (MLsM) / 4 /

-

with various sig- nal-to-noise ratios k

=A/G

and kX=f/Gx.

Y

The values

6,

were equal for a11 points.

The estimates 3

4,

of standard deviations (SD) of the MSP were defined as square roots from diagonal elements of covarian- due to non-linearity and non-stability of

a spectrometer the real values v differ

J

from x If the deviations of v from x

j

3

^J

are normally distributed with the disper- sion

6,

2

,

which characterizes non-linea-

J -9

rity and non-stability of a spectrometer, then the values of v and the spectrum

3

points y, are simulated as ce matrix. Under the same conditions 20 statistically independent spectra were simulated and fitted. From the obtained Here G(S,D) is normally distributed ran- estimates the mean values of parameters

ak

^{and their SD}

b

were calculated.This ak

dom value with the mean S and the disper-

sion D. The function that describes the procedure allowed to estimate the syste-

'spectrum is matic errors of the fitting by a compari-

son of

Zk

with the initial values of MSP.

The values of

3

characterize the real ak

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1980120

c1-112 JOURNAL DE PHYSIQUE

Fig. I.

-2 random errors of parameters measurement.

In general they are not equal to

3 .

ak The results are shown in the fig.l,2.

The solid and dashed curves represent the sign)and width (with positive sign).

CLSM and the MLSM respectively. In Fig. 2 demonstrates the systematic errors fig, 1 the vertical axis is the ratio of 4ak/ak of the CLSM and the MLSM.

5,

^{(a, is A or V or}

^r

^j to SD estimate The MLSM is an approximate method obtained with d.,=0. For the CLSM

4,

^{(see ref.} / 4 / ) , so it has validity limits

the estimate of SD

8a

does not depend We have found that under the condition on

6x

and equals to

&

(does not shown k < 0.2 kx ² the MLSM is valid for M8ssbau-

ak Y

in the figure), but for the MLSM the es- er spectra treatment in the next sense:

A

timate

6,.

is practically identical with a) the iteration procedure of search of

- K

the real SD

5 .

^{So the MLSM} yields the the squares sum minimum practically al-

ak

--

correct estimates of random errors, but ready converges5 ^b) the estimates of SD

-

the CLSM underestimates them, Besides, in

kk

coincide with the real SD

6

; ak the case of relative calibration is used c) the systematic errors are small in the CLSM leads to systematic errors :n comparison with the random errors.

the estimates of amplitude (with negative

R E F E R E N C E S

1. Agresti, D.G. and Belton, M.L., Nucl. Instr. Meth.,

121

(1974), 407.

2, De Waard, H., Rev. Scient. Instr,

,

^{(I 9651, 1728.}

3. Biscar, J.P. ,Kitndig,W. ,Bornme1 ,H. and Hargrove,R.S. ,~ucl. 1nstr.Meth.

,a(

^{1969), 165.}

4. Gavrilov, B.M. and Zemskov, B.G., Nucl, Instr. Meth.,

158

(1979)

,

⁵³¹